Use $x=sec(),$ where since the integrand contains the expression $\sqrt[\phantom{2}]{1+x^2}.$

$(b)$ Apply the substitution $to$ transform the integral into a trigonometric integral. $Do$ not evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^6}{\sqrt[\phantom{2}]{1+x^2}}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(,)d$